On the derivation of homogeneous hydrostatic equations

Emmanuel Grenier

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1999)

  • Volume: 33, Issue: 5, page 965-970
  • ISSN: 0764-583X

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Grenier, Emmanuel. "On the derivation of homogeneous hydrostatic equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.5 (1999): 965-970. <http://eudml.org/doc/193960>.

@article{Grenier1999,
author = {Grenier, Emmanuel},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {two-dimensional incompressible Euler equations; stability of time-independent shear layers flows; energy method; homogeneous hydrostatic equations; convergence; convex profiles; divergence; inflexion profile},
language = {eng},
number = {5},
pages = {965-970},
publisher = {Dunod},
title = {On the derivation of homogeneous hydrostatic equations},
url = {http://eudml.org/doc/193960},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Grenier, Emmanuel
TI - On the derivation of homogeneous hydrostatic equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 5
SP - 965
EP - 970
LA - eng
KW - two-dimensional incompressible Euler equations; stability of time-independent shear layers flows; energy method; homogeneous hydrostatic equations; convergence; convex profiles; divergence; inflexion profile
UR - http://eudml.org/doc/193960
ER -

References

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  1. [1] V.I. Arnold, Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier 16 (1996) 319-361. Zbl0148.45301MR202082
  2. [2] Y. Brenier, Homogeneous hydrostatic flows with convex velocity profiles, Nonlinearity 12 (1999) 495-512. Zbl0984.35131MR1690189
  3. [3] Y. Brenier, Comparaison du régime hydrostatique des fluides incompressibles non visqueux et du régime quasineutre des plasmas. Private communication (1998). 
  4. [4] B. Desjardins, E. Dormy and E. Grenier, Reynolds.m, a matlab package to compute Reynolds numbers of shear layers. Preprint and package, available at http://www.dmi.ens.fr/equipes/edp/reynolds.html. 
  5. [5] S. Friedlander, W. Strauss and M. Vishik, Nonlinear instability in an ideal fluid. Ann. Inst. H. Poincaré. Anal Non Linéaire 14 (1997) 187-209. Zbl0874.76026MR1441392
  6. [6] E. Grenier, On the stability of boundary layers of incompressible Euler equations. J. Differential Equations (to appear). Zbl0958.35106MR1761422
  7. [7] E. Grenier, Boundary layers of 2D inviscid fluids from an Hamiltonian viewpoint. Math. Res. Lett. 6 (1999) 1-13. Zbl0970.76027MR1713128
  8. [8] E. Grenier, On the nonlinear instability of Euler and Navier-Stokes equations (in preparation). Zbl1048.35081
  9. [9] P.-L. Lions, Mathematical topics in fluid Mechanics, Vol I, Incompressible models, in Oxford Lecture Series in Mathematics and its Applications, 3. Oxford Science Publications, The Clarendon Press, Oxford University Press, New York (1996). Zbl0866.76002MR1422251
  10. [10] Lord Rayleigh, On the stability, or instabilité of certain fluid motion. Proc. London Math. Soc. 11 (1880) 57-70. JFM12.0711.02

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